Jean-Luc Mélenchon, the charismatic far-left firebrand whose anti-capitalist stance has seen him rise sharply in the French presidential polls, on Sunday told a vast Paris street rally that France should rise up in a "civic insurrection".

Mélenchon's symbolic open-air rally at the Place de la Bastille, emblem of the French revolution, attracted tens of thousands in a show of force for France's "Left of the Left", buoyed by the financial crisis and disillusionment with the main political parties.

The MEP, who is famous for his scathing, banker-bashing rhetoric, is running for president representing a coalition of leftists which includes the once-powerful Communist party.

A one-time Trotskyist and former teacher, he spent 30 years in the Socialist party, where he served as a minister and senator, before leaving to co-found his own Parti de Gauche - now part of the seven-party alliance Front de Gauche or Leftist Front under whose banner he is seeking the presidency.

He recently surged above the 10% mark in the polls, a sharp rise which has eaten into the score of the Socialist frontrunner François Hollande and delighted the rightwing president Nicolas Sarkozy, who is seeking to exploit differences on the left in his difficult battle for re-election.

Sarkozy has praised Mélenchon's charisma against what he has called the blandness of Hollande.

Mélenchon claims he is winning the ideological battle of the French presidential election, saying his anti-fat cat stance had been mimicked by both Hollande's proposed 75% tax on income over €1m (£830,000) and Sarkozy's promised crackdown on tax exiles.

Hollande and Sarkozy are currently tipped to take the top two places in the 22 April first round and face each other in a 6 May runoff.

Other candidates in the race are the National Front's Marine Le Pen and the centrist François Bayrou.

Mélenchon is locked in a vicious battle with Le Pen for the protest and working class vote. A favourite on TV debate shows for his explosive performances, he directs his most virulent jibes at Le Pen, whom he has called "a bat", "half-demented" and a "dark presence". Last autumn he also accused Hollande of being a "pedal boat captain".

The French left still labours under the shadow of April 2002, when the Socialist candidate was knocked out of the election by the far-right Jean-Marie Le Pen after several leftist candidates fragmented the vote. Pollsters say an upset of that kind is unlikely this year.

But Hollande has recently stressed the importance of voting in the first round for the person most likely to win against Sarkozy, ie himself.

Mélenchon is expected to rally behind Hollande in the second-round runoff. Polls show Hollande would easily win the final vote. Mélenchon could then be considered for a ministerial seat in a future leftwing government.

His manifesto promises include a return to retirement at 60 (from the proposed 62) and capping maximum annual salaries at €360,000, with any earnings above that effectively to be confiscated by the state.

Part of Mélenchon's high showing in the polls comes from the low profile of other far-left and Trotskyist candidates in this election.

The latest poll by Ifop for Le Journal du Dimanche put Sarkozy on 27.5%, Hollande on 27% and Le Pen on 17% in the first round. If the poll is correct, Hollande would beat Sarkozy in the second round by 54% to 46%.

• This article was corrected on 23 March 2012 because it said that Jean-Luc Mélenchon left the Socialist party to found the Front de Gauche; he co-founded the Parti de Gauche. It also gave the upper salary limit as €340,000; the limit is €360,000, after which tax would be set at 100%.